Nonexistence of self-similar blowup for the nonlinear Dirac equations in (1+1) dimensions
We address a general system of nonlinear Dirac equations in (1+1) dimensions and prove nonexistence of classical self-similar blowup solutions in the space of bounded functions. While this argument does not exclude the possibility of finite-time blowup, it still suggests that smooth solutions to the nonlinear Dirac equations in (1+1) dimensions do not develop self-similar singularities in a finite time. In the particular case of the cubic Dirac equations, we characterize (unbounded) self-similar solutions in the closed analytical form.
- Pub Date:
- October 2018
- Mathematics - Analysis of PDEs;
- Mathematical Physics;
- Mathematics - Classical Analysis and ODEs
- 8 pages